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Cost cumulant control: State-feedback, finite-horizon paradigm with application to seismic protection. (English) Zbl 1033.49037
Summary: The paper is concerned with the study of the optimal control which minimizes a finite linear combination of the first $k$ cost cumulants of a finite-horizon integral quadratic form associated with a linear stochastic system, when the controller measures the states. The solution is investigated by adapting dynamic programming techniques to the nontraditional forms evidenced by cumulant representations. The performance of this $k$-cost cumulant $\left(k$CC) controller is compared to that of the best control paradigms published for the American Society of Civil Engineers first-generation structure benchmark for seismically excited buildings; the simulation results indicate that the newly developed control paradigm makes better use of the available control limits and achieves uniform improvement in the officially defined performance statistics for floor vibrations and accelerations.
##### MSC:
 49L20 Dynamic programming method (infinite-dimensional problems) 49N90 Applications of optimal control and differential games 86A15 Seismology